Minor promotion or underpromotion is the promotion of a pawn to a knight, bishop or rook. The player that has moved the pawn to the promotion square has to decide which piece to select: a queen, a rook, a bishop or a knight. It can not remain a pawn and according to the FIDE rules of chess the choice becomes final as soon as the selected piece touches the promotion square.
In almost all games a pawn is promoted to a queen. Sometimes another piece is used, but most of the time this is done without a real need. The player just likes to win with a rook instead of a queen.
But in some cases a minor promotion is needed in order to win the game, most of the time to avoid a stalemate.

The following two diagrams show some easy examples. In the diagram on the left promotion of the pawn to a queen will result in a stalemate, but White can win the game by promoting to a rook (or by playing Kd6). In the diagram on the right promotion to a queen or a rook will result in a draw (stalemate), but promoting to a bishop will result in an easy win. In this case White may also win by playing Ke7.

Another interesting example is shown in the next diagram. Now White is forced to promote. He has to capture the rook. Promoting to a queen or a rook will result in stalemate, so the pawn has to be promoted to a bishop or a knight.

A rather complicated example can be found in the next diagram taken from the game Sokolsky – Ravinsky. This example has been discussed by Tim Krabbé in his article about Practical Underpromotion.

In this article he describes 47 examples of underpromotion in actual games. In the diagram on the left 66.a8=B is winning and it is White’s only winning move. The alternative moves are discussed in Tim Krabbé’s article

Another interesting position that can be found in a number of actual games is the position given in the following diagram.

49.Rc8+ Rxc8 50.b7+ Ka7 will result in a position that should be familiar by now.